To characterize the mean and variance of stochastic concentration distributions in heterogeneous porous media, we derived conservation equations using the first-order perturbation approach and assuming stationary fluc...To characterize the mean and variance of stochastic concentration distributions in heterogeneous porous media, we derived conservation equations using the first-order perturbation approach and assuming stationary fluctuation fields of velocity and concentration. The concentration variance equation, similar to the mean concentration equation, consists of convection and dispersion terms with the mean water velocity and macrodispersivity. In addition, there is a production term in the concentration variance e-quation. The concentration variance production is quadratically proportional to the mean concentration gradient with a coefficient Qij , defined as the concentration variance productivity , which is the difference between the macrodispersivity Aij and the local dispersivity aij multiplied by a four-rank tensor. The macrodispersivity and the local dispersivity, respectively, result in the creation and dissipation of the concentration variance. The concentration variance is produced if the concentration gradient exists. For t→∞, Qij→0 , which indicates that the creation and dissipation of the concentration variance are balanced at large travel time. We solve the variance equation numerically along with the mean e-quation using Aij, Qij, and the effective solute velocity v . The variance productivity increases with the decrease in transverse local dispersivity and is not sensitive to longitudinal local dispersivity. The maximum concentration variance occurs near the maximum mean concentration gradient.展开更多
基金NNSF of China and NSF-EPSCoR of University of Wyoming,USA
文摘To characterize the mean and variance of stochastic concentration distributions in heterogeneous porous media, we derived conservation equations using the first-order perturbation approach and assuming stationary fluctuation fields of velocity and concentration. The concentration variance equation, similar to the mean concentration equation, consists of convection and dispersion terms with the mean water velocity and macrodispersivity. In addition, there is a production term in the concentration variance e-quation. The concentration variance production is quadratically proportional to the mean concentration gradient with a coefficient Qij , defined as the concentration variance productivity , which is the difference between the macrodispersivity Aij and the local dispersivity aij multiplied by a four-rank tensor. The macrodispersivity and the local dispersivity, respectively, result in the creation and dissipation of the concentration variance. The concentration variance is produced if the concentration gradient exists. For t→∞, Qij→0 , which indicates that the creation and dissipation of the concentration variance are balanced at large travel time. We solve the variance equation numerically along with the mean e-quation using Aij, Qij, and the effective solute velocity v . The variance productivity increases with the decrease in transverse local dispersivity and is not sensitive to longitudinal local dispersivity. The maximum concentration variance occurs near the maximum mean concentration gradient.
